The ultra high resolution (12,000 x 15,000 pixel) Bitmap Tiff textures are the best option for Adobe Illustrator.
They offer the highest level of detail, and won't slow down or crash your computer like vector textures can.
For the most authentic look, you will want the texture to “knock out” areas of transparency through your design so the fabric color beneath is visible.
Here’s a tutorial showing how to apply bitmap textures in Adobe Illustrator:
Thrift Mart Bitmap Tiff Textures will look best realistic scaled 9.5” to 14.5” wide. For example, if your t-shirt graphic is 12” wide, size the texture to just cover your graphic.
If you are printing a small graphic (3.5” front pocket hit, for example) just keep your texture scaled at 12” or so. Otherwise, your texture will be too fine for printing.
If you haven't gotten your hands on these textures yet, you can find Thrift Mart here.